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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 3, Pages 451–465 (Mi izv995)  

This article is cited in 3 scientific papers (total in 3 papers)

Breaking solitons. V. Systems of hydrodynamic type

O. I. Bogoyavlenskii


Abstract: A method for constructing the systems of hydrodynamic type having a number of Riemann invariants is indicated. The method is based on a new differential equation in a space of linear operators. The systems of hydrodynamic type naturally connected with the Volterra model and the Toda lattice are constructed. Their continuous limits are found, the equation (see [1] and [2]) of interaction between Riemann breaking waves and transversal long waves is among them. The equations for self-similar solutions of homogeneous systems of hydrodynamic type are derived.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 38:3, 439–454

Bibliographic databases:

UDC: 517.91
MSC: 35Q51, 76B25
Received: 26.02.1991

Citation: O. I. Bogoyavlenskii, “Breaking solitons. V. Systems of hydrodynamic type”, Izv. Akad. Nauk SSSR Ser. Mat., 55:3 (1991), 451–465; Math. USSR-Izv., 38:3 (1992), 439–454

Citation in format AMSBIB
\Bibitem{Bog91}
\by O.~I.~Bogoyavlenskii
\paper Breaking solitons. V.~Systems of hydrodynamic type
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 3
\pages 451--465
\mathnet{http://mi.mathnet.ru/izv995}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1129821}
\zmath{https://zbmath.org/?q=an:0789.35140}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..38..439B}
\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 3
\pages 439--454
\crossref{https://doi.org/10.1070/IM1992v038n03ABEH002209}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JE94100001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. I. Bogoyavlenskii, “Breaking solitons. VI. Extension of systems of hydrodynamic type”, Math. USSR-Izv., 39:2 (1992), 959–973  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. W.X. Ma, “Symmetry constraint of MKdV equations by binary nonlinearization”, Physica A: Statistical Mechanics and its Applications, 219:3-4 (1995), 467  crossref
    3. Zhao Song-Lin, Zhang Da-Jun, Ji Jie, “Exact Solutions for Two Equation Hierarchies”, Chinese Phys Lett, 27:2 (2010), 020201  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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